INTERNATIONL MATHEMATICS AND SCIENCE OLYMPIAD FOR PRIMARY SCHOOLS (IMSO) 2006
INTERNATIONL MATHEMATICS AND SCIENCE OLYMPIAD FOR PRIMARY SCHOOLS (IMSO) 2006. Mathematics Contest in Taiwan, Exploration Problems.
Answer the following 5 questions, and show your detailed solution in the answer sheet. Write down the question number in each paper. Each question is worth 8 points. Time limit: 60 minutes.
1. The solution to each clue of this crossnumber is a two-digit number. None of
these numbers begins with zero. Complete the crossnumber, stating the order in which you solved the clues and explaining why there is only one solution.
Clues Across
1. A square number
3. A multiple of 11
Clues Down
1. A multiple of 7
2. A cube number
2. Notice that 2^2 + 2^2 = 2^3 , so two squares can sum to give a cube; however, the two squares here are equal (to 4).
(a) Find two unequal squares whose sum is a cube.
(b) Show that there are infinitely many pairs of unequal squares whose sum is
equal to a cube.
International Youth Mathematics Contest 2007 HEMIC
This math problemare for students in elementary school. We hope the teachers and students doing this problem. And this problem is for individual contest.
1. The product of two three-digit numbers
2. In a right-angled triangle ACD, the area of shaded region is 10 cm^2, as shown in the figure below. AD = 5 cm, AB = BC, DE = EC. Find the length of AB.
3. A wooden rectangular block, 4 cm × 5 cm × 6 cm, is painted red and then cut into several 1 cm × 1 cm × 1 cm cubes. What is the ratio of the number of cubes with two red faces to the number of cubes with three red faces?
Primary Mathematics World Contest 2006
In this posting, I will share my math problems and this math problems, taken from Primary Mathematics World Contest 2006, that held in Po Leung Kuk. This contest is for individual and I believe you can solve it.
Please read carefully and then take your paper and pencil to do this math problems.
1. Lily plans to spend all of her $31 to buy different types of pens that cost $2, $3 and $4 respectively. If she wants to buy at least 1 pen of each type, what is the maximum number of pens that she can buy?
Answer: 14
2. a, b and c are two-digit numbers. The unit digit of a is 7, the unit digit of b is 5 and the tens digit of c is 1. If a x b + c = 2006, find the value of a + b + c .
3. A class of students bought and equally distributed a certain number of notebooks. If the notebooks are distributed to girls only, each girl will receive 15 notebooks. If the notebooks are distributed to boys only, each boy will receive 10 notebooks. If the notebooks are equally distributed to everyone in the class, how many notebooks will each student receive?
4. The lengths of two sides of a triangle are 2006 and 6002 units respectively. If the length, in the same units, of the third side of this triangle is an integer, how many different triangles can exist?
5. We have four cards numbered 1, 2, 3 and 4 respectively. Three of the four cards are placed into the boxes as shown in the equation below.
How many different values of n can be obtained?
